# Volume occupied by real gases

Molecules of an ideal gas are assumed to have zero volume, the volume available to them for motion is always the same as the volume of the container. In contrast, the molecules of a real gas have small but measurable volumes. At low pressures, the gaseous molecules are relatively far apart, but as the pressure of the gas increases, the intermolecular distances become smaller and smaller . As a result, the volume occupied by the molecules becomes significant compared with the volume of the container. Consequently, the total volume occupied by the gas is greater than the volume predicted by the ideal gas law. Thus at very high pressures, the experimentally measured value of PV/nRT is greater than the value predicted by the ideal gas law.

This is what I read in a website. In the above statements, what is the volume predicted by the ideal gas law? The volume predicted by the gas law, should be the volume of container. Now if volume occupied by real gas is less than the volume of container, how can the volume occupied by it be greater than that predicted by ideal gas law ?

Also, compressibility is given by $Z = \frac{PV}{nRT}$. In this equation is P the measured pressure or the ideal pressure?

When you are "containing" a gas in a container then you are by definition restricting its volume. Lets assume you heat the gas. If the volume is confined then the pressure will increase. Similarly, two different gases will have different pressures if confined to the same volume.

If you somehow control the pressure (there is a movable piston) then a real gas will occupy less volume because of its intermolecular interactions.

Also see this: Volume of different gas in a container

At higher pressures, ideal gas laws consider particles as just points. That means they have more space to fly around, and so for a certain pressure, they need a larger volume. In reality, the particles do have a size. That means they bump into each other/their container more frequently than the ideal gas law would indicate. This bumping means a higher pressure occurs, at a lower volume than predicted.

• Then how to explain the graph I just added above in the question ? – TESLA____ Feb 9 '16 at 5:41
• I realized I wasn't answering your question properly at first. Hopefully this answer makes more sense :) – N A Feb 9 '16 at 5:58

For low pressures, a real gas would be predicted to occupy a slightly smaller volume than an ideal gas since the molecules themselves occupy space for a real gas. However, as we get to higher pressures, the volume of the particles becomes a significant portion of the volume of the container, which makes it much more difficult to compress the gas. We could think of hypothetically compressing an ideal gas to zero volume since its particles take up no space, but we couldn't do the same for a real gas.